Uses in Chemistry
Logarithms can be used in the classroom to calculate the concentration of ions present using either the pH or the pOH of an aqueous solution.
The pH is the measure of the concentration of Hydrogen ions present in an aqueous solution
The pOH is a measure of the concentration of HydrOxide ions present.

Background

As the pH decreases, the concentration of hydrogen ions increases, so the solution becomes more acidic.
As the pH increases, the concentration of hydroxide ions increases, making the solution more alkaline.

 pH [ H+(aq)]                mol per litre 15                       14                       13                       12                       11                       10                        9                        8 1x10-15                   1x10-14                   1x10-13                   1x10-12                   1x10-11                    1x10-10                            1x10-9                   1x10-8 7 1x10-7 6                       5                        4                        3                        2                        1                        0                       -1 1x10-6                    1x10-5                   1x10-4                   1x10-3                   1x10-2                   1x10-1                   1x100                   1x101
NOTE: the pH is equivalent to the power the ten is raised to.

Using the logarithms

By applying the formulas  pH = -log10[ H+ (aq)]  and  pOH = -log10[ OH- (aq)], the concentrations can be calculated.

Example:

pH = 3              pH = -log10[ H+ (aq)]
3 = -log10[ H+ (aq)]          so therefore the H+ concentration
-3 = log10[ H+ (aq)]           is 1x10-3 which by comparing it
10-3 = [ H+ (aq)]                  with the table is correct!

Other useful formulae

• [H+ (aq)] = 1x10-7 moll-1 = [OH- (aq)] in an neutral solution
• pH + pOH = 14
• [H+ (aq)] = 10-pH
A brief history of John Napier               Rules of Logarithms                     Examples of Logarithms
Answers to Examples                   Uses of Logarithms
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